# Emmy Noether

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March 23, 2011

Want to feel like an overpaid slacker? EMMY NOETHER (1882-1935), considered one of the most significant mathematicians of the 20th century, worked for the majority of her career without pay; she was famous for her devotion to mathematics and her students, and her indifference to most everything else. Noether was famed for her ability to abstract and simplify concepts; her research bore fruit in a dozen different mathematical fields, including laying the groundwork for algebraic topology (the study, briefly, of what is unchanged when something is deformed). Mathematicians might quibble, but to physicists, Noether’s crowning contribution is her eponymous theorem, which relates the symmetry of systems to conservation laws (e.g., conservation of energy or angular momentum). Noether’s Theorem turned out to be a fundamental pillar of modern theoretical physics, though it was initially devised in response to a major problem with general relativity. Einstein’s response? “The old guard at [the University of] Göttingen should take some lessons from Miss Noether! She seems to know her stuff.” Fifteen years after she started teaching, Göttingen finally offered Noether a salaried position, which she held for a decade; but in 1933, when Hitler came to power, Noether was one of scores of Jewish faculty who found their professorships revoked. She took a position at Bryn Mawr, but died 18 months later.

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On his or her birthday, HiLobrow irregularly pays tribute to one of our high-, low-, no-, or hilobrow heroes. Also born this date: Erich Fromm.

READ MORE about members of the Psychonauts Generation (1874-83).

As an algebraist I particularly like her development of the “ascending

chain condition” — usually now known as the “Noetherian condition.”

This turns out to be a simple, beautiful condition that tells you

whether an algebraic structure is “simple enough for a human to deal

with.” (I had to deal with non-Noetherian rings a bit in my thesis

and it was a brutal and painful experience.)

The idea: if A is some algebraic structure, Noether’s condition says:

“Suppose you have some substructure of A which we call B, and then

some larger substructure B_1 containing B, and then some still larger

one B_2 containing B_1, and so on and so on… any such chain must be

FINITE.”

A prototypical example is given by positive whole numbers: the fact

that they are Noetherian comes down to the fact that if n is a whole

number, and d is a factor of n, and d_1 is a factor of d, and d_2 is a

factor of d_1, etc…. then eventually you get down to 1 and you have

to stop. There are no infinite chains of factors.

That sounds kind of straightforward but I promise you, if it weren’t

the case, arithmetic would be hell.

Also, I learned from Wikipedia that Noether considered her own Ph.D.

thesis to be a morass of equations, or “Formelngestrupp.” I’m totally

going to start saying that.

Love this comment, thanks Jordan.

jadore emmy nother